1. Field of the Invention
The present invention relates to a method for analyzing the behavior of complex systems, particularly internal combustion engines, by calculating a model which represents various measured variables as a function of input variables, and which has the following basic steps:                selecting various measurement points which correspond to different constellations of measured variables, and performing measurements to ascertain measured variables on a real system;        preparing a model which simulates the dependency of the measured variables on the input variables and calibrating a model on the basis of measured values of the real system obtained at the measurement points.        
2. The Prior Art
In many fields of technology it is necessary to simulate complex systems by models in order to obtain information about the systems and perform development work.
A known problem is frontloading, which is concerned with already integrating simulation and analysis in the early conceptual or design phase of a new product in such a way that as many important development decisions as possible may be secured by simulation, i.e., virtual experiments.
This is important in particular because performing measurements on real systems is complex and the measured values are often not obtained in real time. A standard method for performing simulations comprises simulating the system to be analyzed by a simulation model which reflects the basic behavior of the system. This simulation model is parameterized and calibrated by a number of measured values which were obtained on a real system, so that a sufficiently precise correspondence between simulation model and real system is achieved. After the simulation model is provided, further measured values may be calculated in larger numbers and using less effort.
A method of this type is universally applicable in principle, but is not practicable in all cases. Thus, for example, it is necessary in the field of engine development to develop engine control units at a time in which at least initially there is not yet any real data of the engine available. Only at a later time is it possible to obtain real data on test stands, the amount of this data typically being significantly less than the amount of the data calculable by a simulation model.
In order to be able to simulate complex systems with a minimum amount of precision, it is generally necessary to have a sufficient amount of available data, using which such a model may be calibrated. In the following, measurable variables which may be measured on a real system and, in addition, are to be stimulated by the simulation model in order to be able to study the behavior of the system even without performing further measurements are referred to as measured variables. Typical measured variables in developing internal combustion engines having internal combustion are:                inflowing air mass,        indexed mean pressure,        maximum cylinder pressure, and        exhaust gas temperature pre-catalytic converter and/or turbine.        
The following, into consideration as input variables:                speed        injected fuel quantity        charge temperature        boost pressure        exhaust gas counterpressure        air-fuel ratio in the intake        wall temperatures in the combustion chamber        start of injection        ignition lag        combustion duration        VIBE form factor        
The first five variables may be adopted from the test stand measurements; in contrast, the air-fuel ratio is set to infinity, since no exhaust gas recirculation and therefore no fuel is provided in the intake; the start of injection is read out from the data of the control unit (ECU program maps) during the test stand measurement.
The ignition lag, in order to finally determine the actual start of combustion, the combustion duration, and the form factor are set to estimated values as a function of speed and load in order to describe the VIBE combustion function and thus simulate the combustion. The more precise determination is performed in the course of optimization.
In practice, there are often only a small number of real measured values available, so that it is not meaningfully possible using typical methods to simulate the complex and multivariable relationships between the multiple input variables and the many measured values in a valid way.
Using neuronal networks for the model calculation to simulate the engine behavior in detail is known from M. SCHÜLER, M. HAFNER, and R. ISERMANN: “Einsatz schneller neuronaler Netze zur modellbasierten Optimierung von Verbrennungsmotoren [Use of Rapid Neuronal Networks for Model-Based Optimization of Combustion Engines]”, MTZ 61, 2000, page 2 et seq. In a dynamic process, a model is decomposed into multiple partial models and the partial models are reassembled into a higher-order model. Such a model calculation is extraordinarily complex and takes little consideration of the actual physical relationships of input variables and measured variables.
Furthermore, an article by J. P. VERHOEF and G. P. LEENDERTSE: “Identification of Variables for Site Calibration and Power Curve Assessment in Complex Terrain”, Energy Research Center of the Netherlands, describes preparing simulation models and improving the parameterization using regression methods. With a low number of real measured values, such a method may not achieve any improvement. Similar disadvantages apply for a method as described in M. HAFNER, O. JOST, and R. ISERMANN: “Mechatronic Design Approach for Engine Management Systems”, Darmstadt University of Technology, Institute of Automatic Control.
The object of the present invention is to specify a method which avoids these disadvantages and makes it possible to prepare meaningful models which have a high prognosis quality, even with of a small amount of real ascertained data.